Preheat the oven to 350 F and line a 9x9 pan with parchment paper.
In a large bowl, whisk together the flour, oats, brown sugar, and salt.
Add the butter to the flour mixture and cut it in with a fork, or work the mixture with your hands. Once the mixture takes on a sand-like texture, mix in the egg until fully combined.
Add the blueberries to a saucepan along with the lemon juice and sugar, then let cook over medium heat for about 10 minutes, until the blueberries have burst.
Whisk the cornstarch with two tablespoons water, then pour it into the blueberry mixture. Once the mixture boils and thickens, remove it from heat.
Press half of the crust mixture into the bottom of the pan, then pour the blueberries over top. Crumble the rest of the mixture over the blueberries.
Bake for 35-40 minutes, until the crust has browned. Let cool, then slice and serve.